Factoring Polynomials

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Transcript of Factoring Polynomials

Factoring PolynomialsTrinomial with a Leading Coefficient of 1Since the leading coefficient is 1, the factored form will be of the form: (x )(x )

Find two numbers that multiply to be the constant of the polynomial and add to be the coefficient of x

Fill in the blank spots of each set of parentheses with the two numbers you foundDifference of Two SquaresCheck if a GCF can be factored out.If a polynomial has two terms and uses subtraction, check to see if it is the difference of two squaresIs the first term a monomial times itself?Is the second term a monomial times itself?If the polynomial is of the form a - b , factor it in the following way: (a + b)(a - b)Four-Term PolynomialIf possible, factor out any GCFGroup the first two terms and last two termsFrom each group, factor out the GCF. The remaining binomials should be the same. If not, regroup and try again.Factor out this common binomial term and write your answer.Trinomial with a Leading Coefficient Other than 1Check if a GCF can be factored outMultiply the leading coefficient and the constantFind factors of this product that add together to be the coefficient of xSplit the middle term of the original polynomial with the factorsGroup the first and last two termsFactor the GCF out of each group and write final factored formGCFCheck to see if the polynomial has common factors in each of its termsFactor out the greatest common factor from each termThe polynomial that is left after the GCF has been divided out of each term will be placed in parentheses to be multiplied by the GCFExample4xy +16xy-8y4y(xy + 4x-2)2ExampleFactored:x + 7x + 102Factored:(5)(2)=10 and 5 + 2 =7(x + 2)(x + 5)Example(2x+1)(3x-2)Factored Form:6x - x - 22(6)(-2) = -12Factors of -12 that add to -1: -4 and 36x - 4x + 3x - 222x(3x - 2) + 1(3x - 2)Example(2x + 3)(4x - 1)28x - 2x + 12x - 3322x (4x - 1) + 3(4x - 1)2Factored Form:22ExampleFactored Form:(x + 3)(x - 3)x - 92x = (x)(x)9 = (3)(3)What if it cannot be factored?A polynomial that cannot be factored is called "prime."